Washington — Chris McDaniel came within a few thousand votes of being the next Ted Cruz.

Now, two days after his stunning loss in Mississippi’s high-stakes GOP Senate runoff, Mr. McDaniel risks ruining a potentially bright political future, say both Mississippi and national political observers.

The charismatic, tea party-backed state senator, who took on six-term Sen. Thad Cochran in the marquee primary of 2014, has still refused to concede the race, claiming “voter irregularities.” Thursday afternoon, McDaniel’s campaign called on the state Republican chairman to direct circuit clerks to “cooperate with McDaniel volunteers seeking election data.”

“McDaniel was understandably shell-shocked Tuesday,” writes Sam Hall in the Jackson (Miss.) Clarion Ledger. “His non-concession speech was red meat for his supporters, but it played poorly on the national scene where most were quickly agreeing that this election was over.”

That included groups such as FreedomWorks and the Senate Conservatives Fund. By Wednesday morning, even Senator Cruz, the conservative Texas firebrand, had congratulated “my colleague Thad.”

“As a student of history, I can say that when one goes out a gentleman or a lady, there is a residue of goodwill and they live to fight another day,” says John Gizzi, chief political correspondent of the conservative website Newsmax. “I fear that unless he comes out and embraces Thad by the weekend, Chris McDaniel will not get another opportunity."

In addition, given the successful push by the Cochran campaign to turn out black voters in the runoff, the appearance of trying to disqualify Cochran votes is potentially explosive. This is Mississippi, with a history of racial strife, and where voting rights for African-Americans were hard fought. In one week, the nation celebrates the 50th anniversary of the Civil Rights Act.

McDaniel wants his volunteers to examine the poll books for the June 3 Democratic primary and the June 24 runoff to make sure no one voted illegally. Such a review of the records would need to be monitored by neutral observers trusted by both campaigns, but that aspect was not discussed.

Under Mississippi election law, people who voted in the Democratic primary were not eligible to vote in the Republican runoff. State law also requires voters who participate in a partisan primary to “intend” to vote for that party’s nominee in November, though that law has been deemed unenforceable.

In the June 3 primary, Senator Cochran came in second, barely, and needed to find new votes to beat McDaniel in the second round. Thus, the outreach to Democrats, many of them black, to “cross over” and support Cochran, who is skilled at directing federal money to Mississippi for education, agriculture, and military facilities.

McDaniel lost the runoff by some 6,400 votes, or 2 percentage points. On Tuesday night, he was visibly angry in remarks to his supporters. The next day, he issued a statement.

"In the case of yesterday's election, we must be absolutely certain that our Republican primary was won by Republican voters," McDaniel said. "In the coming days, our team will look into the irregularities to determine whether a challenge is warranted."

Cochran forces who encouraged crossover voting were doing so not just to help their state’s senior senator. They were also engaging in party-building, they said, reaching out to Democrats, blacks, even native Americans.

Republicans outside Mississippi applauded the move. “I’m for more people voting, not less people voting,” Sen. Rand Paul (R) of Kentucky, another tea party icon, said Wednesday.

Mississippi does not register voters by party, and so party labels are earned by voting patterns. And on that basis, deeply red Mississippi is a highly polarized state: Its white population votes mostly Republican and its black population – 37 percent of state residents – votes mostly Democratic.

According to Mr. Hall of the Clarion Ledger, sources close to McDaniel say the group pushing for a challenge is shrinking.

“Even some of his most ardent supporters are starting to worry that moving forward with a challenge will damage his political future and leave the tea party movement in Mississippi without a clear standard-bearer who could lead the charge in 2015,” Hall writes.